Measures Of Central Tendency Flashcards
What is the formula for arithmetic mean for ungrouped data?
X = Σfx/n
What is the formula for the mean of ungrouped data with large frequency?
x̄ = Σfx / Σf
What is the formula for weighted arithmetic mean?
x̄ = ΣWx / ΣW
Where W = the weight
What is the formula for mean for grouped data (with no assumed mean)?
x̄ = Σfx / Σf
What is the formula for mean for grouped data when given assumed mean?
x̄ = A + (Σfd/Σf)
A = assumed mean
d = x - A; where X is class mark
What is the formula for median for ungrouped data when n is odd?
(n+1/2)th value
What is the formula for median for ungrouped data when n is even?
The arithmetic mean of (n/2)th value and (n+2/2)th value.
What is the formula for grouped median?
Lcb + i [ (Σf/2 - Cfb) ÷ f-median ]
Where Lcb = lower class boundary
I = class width
Cfb = cumulative frequency before the median frequency
f-median = frequency of the median class
What is the formula for mode for grouped data?
Lcb + i [(fm - FB) / 2fm - fb - fa]
fm = modal frequency
Fb = frequency before modal frequency
fa = frequency after
What is the empirical relationship for unimodal frequency curves that are moderately skewed?
mean - mode = 3(mean - median)
What is geometric mean?
For a series containing ‘n’ observations, it is the nth root of product of values.
What is the formula for geometric mean in ungrouped data for a set of N positive numbers like X1, X2, X3 … xn? (Expressed in logarithms)
GM = antilog(Σlogx/N)
What is the geometric mean for a set of ungrouped N positive numbers, x1, x2, …, xn? (Without log)
(x1 • x2 • x3 • … • xn)^(1/n)
Therefore, the nth root of the product of the series of numbers.
What is the geometric mean for a set of ungrouped N positive numbers, x1, x2, …, xn (Without log) with corresponding frequencies f1, f2, f3, … fn?
(x1^f1 • x2^f2 • x3^f3 • … • xn^fn)^[1/Σf]
What is the geometric mean for grouped data?
(x1^f1 • x2^f2 • x3^f3 • … • xn^fn)^[1/Σf]
What is the geometric mean for grouped data (with log)?
GM = antilog [(Σf•logx)/Σf]
What is harmonic mean?
This is the reciprocal of the arithmetic mean of the reciprocal of the values of each observation.
What is the formula for harmonic mean for ungrouped data?
HM = N/[Σ(x^-1)]
What is the harmonic mean for ungrouped data with corresponding frequencies?
HM = Σf/[Σf(x^-1)]
What is the formula for harmonic mean for grouped data?
HM = Σf/[Σf(x^-1)]
What is the relationship between arithmetic mean, geometric mean, and harmonic mean?
AM × HM = GM²
What is the formula for grouped population standard deviation?
Formula for sample standard deviation in ungrouped.
Here.
